If it is the bearings then I'm not too bothered as the engine is coming out this winter as a new build is on the cards. That said, the engine has covered relatively small mileage so I would be shocked if the bearings were worn to that extent!

I can happen when the engine is hot so not just on cold start. It could be me just imagining the noise as the light seems to stay on longer sometimes. I have not checked the earth etc but will. Maybe I should clean connections and replace oil pressure sensor first.

In my experience the oil pressure light sending units on Fiat cars, (my experience is with twin cams) does not last more than 50,000 miles or 5-7 years. I suspect that your Fiat Uno Turbo is older than that. If the sender controls the fuel pump, you find out real fast that either you have no oil or the sender went bad. The electric fuel pump will shut off with no oil pump pressure. I do not know if this applies to fuel injected cars but the carb cars have the fuel pump shut off if there is no oil pressure. Change the sending unit and see what happens. Since you are hearing tapping noises it does sound like the oil has drained down away from the tappets and into the sump or there is too much clearance in the pump or the engine bearings. I would check out the bottom end before the crank gets damaged.
Tom

In an ideal situation the gauge flickers into life and registers pressure before the preset-pressure of the oil warning light is reached. The response should be a few seconds tops. Faster when cold?

Not really. The engine spins faster when hot. There is no fixed rule. Either way the oil pressure gauge should flicker into life almost instantly.

Fiat instruments from the 70s are completely USELESS! They are made from compliant materials that go stiff and give errant readings in ALL SITUATIONS!

Senders and gauges.

Stop guessing and hoping for the best here. Fit all new instruments and senders and then and only then hope for the best - but I think I will be proved right and this engine needs an exploratory strip to check the bearings.